Amumu should focus on controlled first clears and avoid early river fights without lane priority to survive Shyvana's faster tempo and dueling power.
Prioritize setting up (Q) ganks on lanes with priority and use (R) to turn grouped objective fights in your favor as the game scales into mid and late phases.
Jungle Plan
Path for controlled clears and look to gank lanes with priority using your (Q) to force Shyvana off camps or objectives early.
Contest first Scuttle only if your lanes can move first; otherwise, focus on defensive vision and counter-ganking Shyvana's early river moves.
Use your (R) to lock down grouped enemies during dragon or Rift Herald fights, converting jungle tempo into objective control and scaling denial.
Danger windows
Beware early invade attempts around level 3 when Shyvana's clear speed and dueling power can overwhelm you if lanes lack priority.
Avoid isolated river skirmishes before level 6 where Shyvana's mobility and (R) displacement can punish you.
Be cautious contesting dragon early without lane priority, as Shyvana's objective control and scaling can force unfavorable fights.
Early game
Start with a full or three-camp clear aimed at lanes that can follow your (Q) engage to secure early ganks.
Avoid contesting first Scuttle if nearby lanes lack priority; instead, ward defensively to prevent Shyvana invades.
Delay river fights until level 6 when (R) can secure objective control and counter Shyvana's dragon-form power spike.
Power spikes
At level 6, Amumu's (R) provides strong teamfight lockdown; use this to force grouped fights around objectives.
Shyvana's mid-game dragon-form spike increases her dueling and objective threat; respect this by avoiding isolated fights and focusing on grouped defense.
Amumu's medium clear speed requires careful tempo management to avoid losing jungle pressure to Shyvana's faster farming.
Win conditions
Survive early jungle pressure by securing safe clears and leveraging lanes with priority to set up (Q) ganks.
Use (R) to force grouped fights around dragon, Rift Herald, or Void Grubs, turning your crowd control into objective control and teamfight lockdown.
Deny Shyvana free farm and scaling by counter-jungling when safe and coordinating with lanes to punish her slower early game pressure.
Tip: For Amumu vs Shyvana, read overview, trading pattern, and danger windows first for a fast Jungle lane check.